c) (5 points) shafts are cut to a critical length by two machines: A and B. Each

Question

c) (5 points) shafts are cut to a critical length by two machines: A and B. Each machine cuts 50% of all shafts, and each machine accomplishes its task in approximately the same amount of time. Machine A's shafts are mostly good, but machine B's shafts are mostly defective. As shafts are finished, they are placed on the conveyor belt and fall into a bin, which can hold 100 shafts. Once a bin is filled, a new one is placed at the end of the conveyor to take its place. Consequently, approximately 50% of the shafts in any bin are from machine A and the other 50% are from machine B. The bins are taken to the next operation (Figure 1 presents a schematic of the shaft-cutting system). Employees at this next operation have started to complain about defective shafts. Thus, an inspection station is set up, and control chart is designed from 100% inspection of every 20th bin as shown in Figure 2, Do you think that the process is in statistical control?-justify your answer with logical explanation.

Explanation / Answer

Reading the proportion of defectives figures from the given graph, the average proportion, say pcap, is found to be 0.5. As indicated in the question, each proportion is based on a production of 100 (n) units.

Hence, control limits for the p-chart would be: pcap ± 3{pcap(1 - pcap)/n}

= 0.5 ± 3(0.5 x 0.5/100)

= 0.5 ± (3 x 0.05)

= (0.35, 0.65)

Since all the proportion of defectives figures from the given graph are within these limits, it is fair to assume that the process is under control. ANSWER

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